Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at an increasing rate over time.

Front

What is exponential decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

Front

What does the initial value represent in an exponential function?

Back

The initial value is the starting amount before any growth or decay occurs, often represented as 'a' in the function y = a(1 + r)^x.

Front

In the function y = a(1 + r)^x, what does 'r' represent?

Back

'r' represents the rate of growth (if positive) or decay (if negative) expressed as a decimal.

Front

How do you convert a percentage increase to a decimal for use in exponential functions?

Back

To convert a percentage increase to a decimal, divide the percentage by 100. For example, a 35% increase becomes 0.35.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time period.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is the time period.

Front

How do you determine the amount after a certain number of years in an exponential function?

Back

Substitute the number of years for 'x' in the exponential function and calculate the value of 'y'.

Front

What does the graph of an exponential growth function look like?

Back

The graph of an exponential growth function rises steeply and continuously increases, starting from the initial value.

Front

What does the graph of an exponential decay function look like?

Back

The graph of an exponential decay function starts at the initial value and gradually approaches zero, never actually reaching it.